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This one is a bit of a stumper. Since there are no measurements whatsoever you really have nothing but visual cues to go on and maybe a few simple rules. THis is not a math problem but a logic problem.

THe only things we can know for sure is that a+b+c=180 degrees as should b+d+e. We can assume that a, b and c are not equal due to the lean of the triangle and that A and C are not equal. By the wording of the question you can eliminate A,C and d as possible answers so it has to be B or D since they are the only choices with "pairs" of angles. Now since B is the same for both we can surmise that d+e=a+c.

Now IF c=d and d=e then c=e and since we know that c+b+a=180 and d+e+b=180 then we can also surmise that a is equal to c,d and e. Therefore since answer E does not allow for a to be equal to any of them the answer is "B". If a and e are equal then a+b=e+b therefore d+b=c+b. B is the only answer that logically allows for all angles to be considered in the equation.

I asked my brother, who's rather good with this sort of thing. Here's what he said:

Quote

There are theorems that the angle between a tangent and a cord is half the subtended arc, as is the inscribed angle. So a=e, c=d.Proof: Draw a triangle with base db and opposite side the center of the circle, noting that it is an isosceles triangle with central angle the angle of the arc bd and the other angles equal to the complement of a (since a radius and a tangent meet in a right angle). The central angle is thus 180-2comp(a)=180-2(90-a)=2a.The other (that e is half the angle of the inscribed arc) is a standard theorem, and looks a bit harder to prove.

By the wording of the question you can eliminate A,C and d as possible answers so it has to be B or D since they are the only choices with "pairs" of angles.

You happen to exclude wrong answers and leave the correct answer, but this logic is just faulty. The question does not say the answer will contain "pairs." The set of five possible answers contains "pairs."

Well, I had forgotten whatever they had tried to force into me at school about angles of chords, so this is how I worked it out....

Draw lines from the vertices of the triangles to the centre of the circle. This splits the triangle up into three isoceles triangles (triangles with two equal sides and angles). Label the equal angles of the upper isoceles triangle "p", the equal angles of the isoceles triangle to the right "q" and the equal angles of the isoceles triangle to the left "r".

...This is "kite related" for me, in that I have tried and tried to do tricks by trying to copy the actions of others, but usually failed at that. The way my mind works, I have had to learn what little I have learnt by trying to figure out what is going on - how the kite can fly.Hey, ho. Bet the USA SATs don't work it out in the above way....

My opinion has always been it doesn't matter which road you take if you arrive at your destination ... I never did too well in math either, the right answer never seemed to satisfy the teacher because the convoluted road I took to get there always confused them I think mine was more scenic though

Logged

"Living is easy with eyes closed, misunderstanding all you see" John W Lennon

"People do not quit playing because they grow old, they grow old because they quit playing" George Bernard Shaw

By the wording of the question you can eliminate A,C and d as possible answers so it has to be B or D since they are the only choices with "pairs" of angles.

You happen to exclude wrong answers and leave the correct answer, but this logic is just faulty. The question does not say the answer will contain "pairs." The set of five possible answers contains "pairs."

Actually no only B and D contain pairs, the other contain "a" pair. Most, if not all multiple choice math questions are worded so you can pretty much eliminate 60% of the answers right off. Once you know the most likely answers you can work backwards like I did to see which one is ultimately correct.

By the wording of the question you can eliminate A,C and d as possible answers so it has to be B or D since they are the only choices with "pairs" of angles.

You happen to exclude wrong answers and leave the correct answer, but this logic is just faulty. The question does not say the answer will contain "pairs." The set of five possible answers contains "pairs."

Actually no only B and D contain pairs, the other contain "a" pair. Most, if not all multiple choice math questions are worded so you can pretty much eliminate 60% of the answers right off. Once you know the most likely answers you can work backwards like I did to see which one is ultimately correct.

I know we're both just repeating our positions here, but..."Following pairs" means there are multiple to choose from. It does not necessarily mean the answer contains pairs. I'll admit you can parse it that way, but only because the verb is not one that indicates the number of the noun. (And the noun itself, "which", is no help, either.) However, the answer is not required to be one that contains multiple pairs.

By the wording of the question you can eliminate A,C and d as possible answers so it has to be B or D since they are the only choices with "pairs" of angles.

You happen to exclude wrong answers and leave the correct answer, but this logic is just faulty. The question does not say the answer will contain "pairs." The set of five possible answers contains "pairs."

Actually no only B and D contain pairs, the other contain "a" pair. Most, if not all multiple choice math questions are worded so you can pretty much eliminate 60% of the answers right off. Once you know the most likely answers you can work backwards like I did to see which one is ultimately correct.

I know we're both just repeating our positions here, but..."Following pairs" means there are multiple to choose from. It does not necessarily mean the answer contains pairs. I'll admit you can parse it that way, but only because the verb is not one that indicates the number of the noun. (And the noun itself, "which", is no help, either.) However, the answer is not required to be one that contains multiple pairs.

Your right, but from having a mother, who is also a teacher, I have seen a lot of standardized tests. From my experience it's common for them to be worded to indicate what answers can be eliminated or if any can be. Saying "which answer" or "which of these answers" if there is only one right or "which answers" if more than one. On similar geometry/calculous questions if its only one set of angles they are looking for it will usually say "which of these angles are the same" or "which pair of angles". It doesn't always hold true but I'd say a good 95% of the time the question will clue you in to the most likely answer. Even More so in the last few years they seem to be making it easier to guess correctly by how they word the questions.

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